The existence of fold and flip bifurcations can be verified directly by solving \(\mu (v) = 1\)  and \(\mu (v) = -1\)  respectively for \(v\) , where \(\mu (v)\)  is given by (REF ), and by checking the relevant non-degeneracy conditions in e.g. [1]} and [1]} respectively. Details and explicit calculations are given in [3]}.
